Finite Math Examples

$y = 7 x - 9$ , $(8, 3)$

Step 1

Use the slope-intercept form to find the slope.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is $7$ .

$m = 7$

Step 2

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{7}$

Step 3

Find the equation of the perpendicular line using the point-slope formula.

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Step 3.1

Use the slope $- \frac{1}{7}$ and a given point $(8, 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = - \frac{1}{7} \cdot (x - (8))$

Step 3.2

Simplify the equation and keep it in point-slope form.

$y - 3 = - \frac{1}{7} \cdot (x - 8)$

Step 4

Write in $y = m x + b$ form.

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Step 4.1

Solve for $y$ .

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Step 4.1.1

Simplify $- \frac{1}{7} \cdot (x - 8)$ .

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Step 4.1.1.1

Rewrite.

$y - 3 = 0 + 0 - \frac{1}{7} \cdot (x - 8)$

Step 4.1.1.2

Simplify by adding zeros.

$y - 3 = - \frac{1}{7} \cdot (x - 8)$

Step 4.1.1.3

Apply the distributive property.

$y - 3 = - \frac{1}{7} x - \frac{1}{7} \cdot - 8$

Step 4.1.1.4

Combine $x$ and $\frac{1}{7}$ .

$y - 3 = - \frac{x}{7} - \frac{1}{7} \cdot - 8$

Step 4.1.1.5

Multiply $- \frac{1}{7} \cdot - 8$ .

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Step 4.1.1.5.1

Multiply $- 8$ by $- 1$ .

$y - 3 = - \frac{x}{7} + 8 (\frac{1}{7})$

Step 4.1.1.5.2

Combine $8$ and $\frac{1}{7}$ .

$y - 3 = - \frac{x}{7} + \frac{8}{7}$

Step 4.1.2

Move all terms not containing $y$ to the right side of the equation.

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Step 4.1.2.1

Add $3$ to both sides of the equation.

$y = - \frac{x}{7} + \frac{8}{7} + 3$

Step 4.1.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{x}{7} + \frac{8}{7} + 3 \cdot \frac{7}{7}$

Step 4.1.2.3

Combine $3$ and $\frac{7}{7}$ .

$y = - \frac{x}{7} + \frac{8}{7} + \frac{3 \cdot 7}{7}$

Step 4.1.2.4

Combine the numerators over the common denominator.

$y = - \frac{x}{7} + \frac{8 + 3 \cdot 7}{7}$

Step 4.1.2.5

Simplify the numerator.

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Step 4.1.2.5.1

Multiply $3$ by $7$ .

$y = - \frac{x}{7} + \frac{8 + 21}{7}$

Step 4.1.2.5.2

Add $8$ and $21$ .

$y = - \frac{x}{7} + \frac{29}{7}$

Step 4.2

Reorder terms.

$y = - (\frac{1}{7} x) + \frac{29}{7}$

Step 4.3

Remove parentheses.

$y = - \frac{1}{7} x + \frac{29}{7}$

Step 5